GPS Analysis
Najja Osiomwan
10/27/2020
Google Play Store Analysis
This is an exploratory data analysis project to examine how different variables such as the size or the price of an app affect the ratings and amount of reviews or installs an app recieves. After exploring the relationship between variables I will attempt to answer some questions about the data by testing for significance and create a linear regression model that can predict the amount of install an app will recieve based on the variables available in the dataset.
Data Cleaning
library(psych)
library(ggplot2)##
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## %+%, alphalibrary(gmodels)
library(MASS)
library(car)## Loading required package: carData##
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## logitlibrary(cluster)
library(fpc)
library(corrplot)## corrplot 0.84 loadedlibrary(FactoMineR)
library(corrplot)
library(scatterplot3d)
library(readr)
library(lubridate)##
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## datelibrary(tidyr)
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## intersect, setdiff, setequal, unionlibrary(zoo)##
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## as.Date, as.Date.numericlibrary(Hmisc)## Loading required package: lattice## Loading required package: survival## Loading required package: Formula##
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## lowesslibrary(mosaicCore)##
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library(plotrix)##
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## rescaleg_apps <- read.csv("Google-Playstore-Full.csv", header = T)
head(g_apps)## App.Name Category
## 1 DoorDash - Food Delivery FOOD_AND_DRINK
## 2 TripAdvisor Hotels Flights Restaurants Attractions TRAVEL_AND_LOCAL
## 3 Peapod SHOPPING
## 4 foodpanda - Local Food Delivery FOOD_AND_DRINK
## 5 My CookBook Pro (Ad Free) FOOD_AND_DRINK
## 6 Safeway Online Shopping FOOD_AND_DRINK
## Rating Reviews Installs Size Price Content.Rating
## 1 4.548561573 305034 5,000,000+ Varies with device 0 Everyone
## 2 4.400671482 1207922 100,000,000+ Varies with device 0 Everyone
## 3 3.656329393 1967 100,000+ 1.4M 0 Everyone
## 4 4.107232571 389154 10,000,000+ 16M 0 Everyone
## 5 4.647752285 2291 10,000+ Varies with device $5.99 Everyone
## 6 3.82532239 2559 100,000+ 23M 0 Everyone
## Last.Updated Minimum.Version Latest.Version X X.1 X.2 X.3
## 1 March 29, 2019 Varies with device Varies with device NA
## 2 March 29, 2019 Varies with device Varies with device NA
## 3 September 20, 2018 5.0 and up 2.2.0 NA
## 4 March 22, 2019 4.2 and up 4.18.2 NA
## 5 April 1, 2019 Varies with device Varies with device NA
## 6 March 29, 2019 5.0 and up 7.6.0 NAstr(g_apps)## 'data.frame': 267052 obs. of 15 variables:
## $ App.Name : Factor w/ 244406 levels "_PRISM","--SB Kiosk App--",..: 74410 223974 168267 91440 153012 191111 241995 213156 86853 29047 ...
## $ Category : Factor w/ 68 levels ""," Accounting",..: 30 66 61 30 30 30 66 30 66 30 ...
## $ Rating : Factor w/ 99856 levels " Economics"," Lessons",..: 75011 58414 11903 30767 85185 16562 44402 69013 16127 74642 ...
## $ Reviews : Factor w/ 24545 levels "","1","10","100",..: 11780 2011 7233 14352 8799 9912 15192 3790 22757 20222 ...
## $ Installs : Factor w/ 38 levels " Xmax X","0+",..: 23 12 13 9 10 13 9 23 10 23 ...
## $ Size : Factor w/ 1248 levels "1,000,000+","1,000+",..: 1248 1248 31 153 1248 248 1248 1248 454 1248 ...
## $ Price : Factor w/ 504 levels "$0.56","$0.67",..: 488 488 488 488 398 488 488 488 488 488 ...
## $ Content.Rating : Factor w/ 12 levels "$0.99","$2.49",..: 8 8 8 8 8 8 11 8 8 8 ...
## $ Last.Updated : Factor w/ 2751 levels "0","500,000+",..: 1761 1761 2621 1706 12 1761 1753 1786 698 1820 ...
## $ Minimum.Version: Factor w/ 100 levels "","0","1.0 - 6.0",..: 100 100 80 70 100 80 100 100 72 100 ...
## $ Latest.Version : Factor w/ 22994 levels ""," 1.0.1.6",..: 22890 22890 11185 16974 22890 20210 22890 22890 11936 22890 ...
## $ X : Factor w/ 16 levels "","1.0.0","1.0.1",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ X.1 : Factor w/ 4 levels "","1","4.4 and up",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ X.2 : Factor w/ 3 levels "","4.4 and up",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ X.3 : num NA NA NA NA NA NA NA NA NA NA ...summary(g_apps)## App.Name Category Rating
## ???? : 766 EDUCATION : 33394 5 : 23804
## ????? : 635 TOOLS : 21592 4 : 5469
## ?????? : 608 BOOKS_AND_REFERENCE: 21377 4.5 : 3519
## ??????? : 415 ENTERTAINMENT : 20604 3 : 2581
## ????????: 334 MUSIC_AND_AUDIO : 17876 4.333333492: 2204
## (Other) :264293 LIFESTYLE : 15034 4.666666508: 2167
## NA's : 1 (Other) :137175 (Other) :227308
## Reviews Installs Size
## 1 : 9203 10,000+ :60531 Varies with device: 11726
## 2 : 7581 1,000+ :48880 11M : 7312
## 3 : 6445 100,000+:37498 12M : 6362
## 4 : 5624 5,000+ :26360 13M : 5569
## 5 : 4962 50,000+ :22795 14M : 5266
## 6 : 4479 100+ :18502 15M : 5157
## (Other):228758 (Other) :52486 (Other) :225660
## Price Content.Rating Last.Updated
## 0 :255428 Everyone :241578 April 2, 2019 : 4000
## $0.99 : 2317 Teen : 17261 April 1, 2019 : 3331
## $1.99 : 1552 Everyone 10+: 4661 March 28, 2019: 2736
## $2.99 : 1351 Mature 17+ : 3489 March 25, 2019: 2681
## $4.99 : 883 Unrated : 33 March 29, 2019: 2670
## $3.99 : 767 0 : 12 March 26, 2019: 2650
## (Other): 4754 (Other) : 18 (Other) :248984
## Minimum.Version Latest.Version
## 4.1 and up :70848 1 : 33002
## 4.0.3 and up:49324 1.1 : 11714
## 4.0 and up :37837 Varies with device: 8555
## 4.4 and up :28250 1.2 : 8205
## 5.0 and up :17413 2 : 7126
## 4.2 and up :13629 1.3 : 5922
## (Other) :49751 (Other) :192528
## X X.1
## :267034 :267049
## 1.0.0 : 2 1 : 1
## 1.0.1 : 2 4.4 and up : 1
## Varies with device: 2 February 14, 2019: 1
## 1.1 : 1
## 1.15.1 : 1
## (Other) : 10
## X.2 X.3
## :267050 Min. :9.1
## 4.4 and up: 1 1st Qu.:9.1
## 9.0.3 : 1 Median :9.1
## Mean :9.1
## 3rd Qu.:9.1
## Max. :9.1
## NA's :267051Looks like there are some rows with misaligned data and columns 12, 13, 14 and 15 are all NA (completely blank) so I’ll remove those columns.
# Removing misaligned rows
m1 <- which(as.character(g_apps$X) == "1.0.0")
m2 <- which(as.character(g_apps$X) == "1.0.1")
m3 <- which(as.character(g_apps$X) == "Varies with device")
m4 <- which(as.character(g_apps$X) == "1.1")
m5 <- which(as.character(g_apps$X) == "1.15.1")
m6 <- which(as.character(g_apps$X) == "1.2")
m7 <- which(as.character(g_apps$X) == "1.54")
m8 <- which(as.character(g_apps$X) == "1.6")
m9 <- which(as.character(g_apps$X) == "2.2.0")
m10 <- which(as.character(g_apps$X) == "2.3")
m11 <- which(as.character(g_apps$X) == "4.0.0.0")
m12 <- which(as.character(g_apps$X) == "4.0.1")
m13 <- which(as.character(g_apps$X) == "4.0.3 and up")
m14 <- which(as.character(g_apps$X) == "April 2, 2019")
m15 <- which(as.character(g_apps$X) == "Everyone")
m16 <- which(as.character(g_apps$X) == "Varies with device")
misaligned <- c(m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12, m13, m14, m15, m16)
g_apps1 <- g_apps[-misaligned, ]
head(g_apps1) # Columns X - X.3 are now empty, let's drop those columns from the dataset## App.Name Category
## 1 DoorDash - Food Delivery FOOD_AND_DRINK
## 2 TripAdvisor Hotels Flights Restaurants Attractions TRAVEL_AND_LOCAL
## 3 Peapod SHOPPING
## 4 foodpanda - Local Food Delivery FOOD_AND_DRINK
## 5 My CookBook Pro (Ad Free) FOOD_AND_DRINK
## 6 Safeway Online Shopping FOOD_AND_DRINK
## Rating Reviews Installs Size Price Content.Rating
## 1 4.548561573 305034 5,000,000+ Varies with device 0 Everyone
## 2 4.400671482 1207922 100,000,000+ Varies with device 0 Everyone
## 3 3.656329393 1967 100,000+ 1.4M 0 Everyone
## 4 4.107232571 389154 10,000,000+ 16M 0 Everyone
## 5 4.647752285 2291 10,000+ Varies with device $5.99 Everyone
## 6 3.82532239 2559 100,000+ 23M 0 Everyone
## Last.Updated Minimum.Version Latest.Version X X.1 X.2 X.3
## 1 March 29, 2019 Varies with device Varies with device NA
## 2 March 29, 2019 Varies with device Varies with device NA
## 3 September 20, 2018 5.0 and up 2.2.0 NA
## 4 March 22, 2019 4.2 and up 4.18.2 NA
## 5 April 1, 2019 Varies with device Varies with device NA
## 6 March 29, 2019 5.0 and up 7.6.0 NAg_apps1 <- g_apps1[,-c(12, 13, 14,15)]
summary(g_apps1)## App.Name Category Rating
## ???? : 766 EDUCATION : 33394 5 : 23804
## ????? : 635 TOOLS : 21592 4 : 5469
## ?????? : 608 BOOKS_AND_REFERENCE: 21377 4.5 : 3519
## ??????? : 415 ENTERTAINMENT : 20604 3 : 2581
## ????????: 334 MUSIC_AND_AUDIO : 17876 4.333333492: 2204
## (Other) :264275 LIFESTYLE : 15034 4.666666508: 2167
## NA's : 1 (Other) :137157 (Other) :227290
## Reviews Installs Size
## 1 : 9203 10,000+ :60531 Varies with device: 11726
## 2 : 7581 1,000+ :48880 11M : 7312
## 3 : 6445 100,000+:37498 12M : 6362
## 4 : 5622 5,000+ :26360 13M : 5569
## 5 : 4960 50,000+ :22795 14M : 5266
## 6 : 4479 100+ :18502 15M : 5157
## (Other):228744 (Other) :52468 (Other) :225642
## Price Content.Rating Last.Updated
## 0 :255428 Everyone :241578 April 2, 2019 : 4000
## $0.99 : 2317 Teen : 17261 April 1, 2019 : 3331
## $1.99 : 1552 Everyone 10+ : 4661 March 28, 2019: 2736
## $2.99 : 1351 Mature 17+ : 3489 March 25, 2019: 2681
## $4.99 : 883 Unrated : 33 March 29, 2019: 2670
## $3.99 : 767 Adults only 18+: 12 March 26, 2019: 2650
## (Other): 4736 (Other) : 0 (Other) :248966
## Minimum.Version Latest.Version
## 4.1 and up :70848 1 : 33002
## 4.0.3 and up:49324 1.1 : 11714
## 4.0 and up :37837 Varies with device: 8553
## 4.4 and up :28250 1.2 : 8205
## 5.0 and up :17413 2 : 7126
## 4.2 and up :13629 1.3 : 5922
## (Other) :49733 (Other) :192512Formating the data for analysis.
g_apps2 <- g_apps1
# Removing k and M from Size variable
g_apps2$Size <- as.character(g_apps2$Size)
g_apps2$Size <- gsub("\\.5k", "500", g_apps2$Size)
g_apps2$Size <- gsub("\\.1M", "100000", g_apps2$Size)
g_apps2$Size <- gsub("\\.2M", "200000", g_apps2$Size)
g_apps2$Size <- gsub("\\.3M", "300000", g_apps2$Size)
g_apps2$Size <- gsub("\\.4M", "400000", g_apps2$Size)
g_apps2$Size <- gsub("\\.5M", "500000", g_apps2$Size)
g_apps2$Size <- gsub("\\.6M", "600000", g_apps2$Size)
g_apps2$Size <- gsub("\\.7M", "700000", g_apps2$Size)
g_apps2$Size <- gsub("\\.8M", "800000", g_apps2$Size)
g_apps2$Size <- gsub("\\.9M", "900000", g_apps2$Size)
g_apps2$Size <- gsub("\\.0M","000000",g_apps2$Size)
g_apps2$Size <- gsub("\\M", "000000", g_apps2$Size)
g_apps2$Size <- gsub("\\k", "000", g_apps2$Size)
g_apps2$Size <- gsub("\\,", "", g_apps2$Size)
g_apps2$Size <- gsub("\\+", "", g_apps2$Size)
g_apps2$Size <- as.factor(g_apps2$Size)
# Removing + and , from Installs
g_apps2$Installs <- gsub("\\+", "", g_apps2$Installs)
g_apps2$Installs <- gsub(",", "", g_apps2$Installs)
g_apps2$Installs <- as.factor(g_apps2$Installs)
# Remove the $ from Price
g_apps2$Price <- gsub("\\$", "", g_apps2$Price)
g_apps2$Price <- as.factor(g_apps2$Price)
# Change last updated to date format
g_apps2$Last.Updated <- gsub("January", "1-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("February", "2-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("March", "3-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("April", "4-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("May", "5-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("June", "6-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("July", "7-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("August", "8-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("September", "9-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("October", "10-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("November", "11-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub("December", "12-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub(",", "-", g_apps2$Last.Updated)
g_apps2$Last.Updated <- gsub(" ", "", g_apps2$Last.Updated)
g_apps2$Last.Updated <- strptime(g_apps2$Last.Updated,format="%m-%d-%Y")
g_apps2$Last.Updated <- as.Date(g_apps2$Last.Updated, format = "%d-%m-%y")
# Remove "and up" from Minimum Version
g_apps2$Minimum.Version <- gsub(" and up", "+", g_apps2$Minimum.Version)
g_apps2$Minimum.Version <- as.factor(g_apps2$Minimum.Version)
summary(g_apps2)## App.Name Category Rating
## ???? : 766 EDUCATION : 33394 5 : 23804
## ????? : 635 TOOLS : 21592 4 : 5469
## ?????? : 608 BOOKS_AND_REFERENCE: 21377 4.5 : 3519
## ??????? : 415 ENTERTAINMENT : 20604 3 : 2581
## ????????: 334 MUSIC_AND_AUDIO : 17876 4.333333492: 2204
## (Other) :264275 LIFESTYLE : 15034 4.666666508: 2167
## NA's : 1 (Other) :137157 (Other) :227290
## Reviews Installs Size
## 1 : 9203 10000 :60531 Varies with device: 11726
## 2 : 7581 1000 :48880 11000000 : 7312
## 3 : 6445 100000 :37498 12000000 : 6362
## 4 : 5622 5000 :26360 13000000 : 5569
## 5 : 4960 50000 :22795 14000000 : 5266
## 6 : 4479 100 :18502 15000000 : 5157
## (Other):228744 (Other):52468 (Other) :225642
## Price Content.Rating Last.Updated
## 0 :255428 Everyone :241578 Min. :2009-02-11
## 0.99 : 2317 Teen : 17261 1st Qu.:2018-04-30
## 1.99 : 1552 Everyone 10+ : 4661 Median :2018-11-20
## 2.99 : 1351 Mature 17+ : 3489 Mean :2018-06-22
## 4.99 : 883 Unrated : 33 3rd Qu.:2019-02-22
## 3.99 : 767 Adults only 18+: 12 Max. :2019-04-04
## (Other): 4736 (Other) : 0
## Minimum.Version Latest.Version
## 4.1+ :70848 1 : 33002
## 4.0.3+ :49324 1.1 : 11714
## 4.0+ :37837 Varies with device: 8553
## 4.4+ :28250 1.2 : 8205
## 5.0+ :17413 2 : 7126
## 4.2+ :13629 1.3 : 5922
## (Other):49733 (Other) :192512Univariate Analysis
Now I’ll take a look at each variable and check for a normal distribution since the tests I’ll be performing assume normal distribution.
g_apps2$Rating <- as.numeric(as.character(g_apps2$Rating))
g_apps2$Reviews <- as.numeric(as.character(g_apps2$Reviews))
g_apps3 <- g_apps2
# -------- Rating ----------#
rating <- g_apps3$Rating
hist(rating, breaks = 100, col="#00DCFF")
summary(rating)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.000 4.018 4.382 4.269 4.649 5.000len_rate <- length(which(rating>=3))
len_rateP <- len_rate/(length(rating))
len_rateP # 96.9% of apps are rating 3 or higher## [1] 0.9695095# Look for normal distribution
par(mfrow=c(3,1))
plot(density(rating, na.rm = T))
plot(density(log(rating), na.rm = T))
plot(density(sqrt(rating), na.rm = T)) 
low_outliers <- fivenum(rating, na.rm = T)[2]-IQR(rating, na.rm = T)*1.5
low_outliers # 3.07## [1] 3.071228low <- which(rating < low_outliers)
length(low) # 11627 lower outliers because the data is left skewed, removing for normal distribution## [1] 11627We can see that the all transformations of the data are skewed, so I’ll try removing low outliers
g_apps4 <- g_apps3[-low,]
par(mfrow=c(1,1))
hist(g_apps4$Rating, col = c("#00DCFF"), main = "Distribution of Ratings", breaks = 100)
plot(density(g_apps4$Rating, na.rm = T), col = "#444444")
plot(density(log(g_apps4$Rating), na.rm = T), col="#444444", lwd=2.5)
plot(density(sqrt(g_apps4$Rating), na.rm = T), col="#444444", lwd=2.5)
hist(g_apps4$Rating, col=c("#00DCFF"), xlim=c(3,5), freq = F, breaks=seq(.5, 20, 0.1),
xlab = "App Rating", main = "Distribution of App Ratings")
rug(jitter(g_apps4$Rating), col="#444444")
lines(density(g_apps4$Rating), col="#FFD800", lwd=2)
box()
boxplot(g_apps4$Rating, main="Ratings", col="#00DCFF")
The ratings are still left skewed, but I will leave it as is.
# --------- Category --------#
cat <- table(g_apps4$Category)
sortcat <- sort(cat, decreasing = TRUE)
pcat <- round(prop.table(cat), 2)
pcat <- sort(pcat, decreasing = TRUE)
pcat##
## EDUCATION BOOKS_AND_REFERENCE
## 0.13 0.08
## ENTERTAINMENT TOOLS
## 0.08 0.08
## MUSIC_AND_AUDIO LIFESTYLE
## 0.07 0.06
## BUSINESS FINANCE
## 0.04 0.04
## PERSONALIZATION HEALTH_AND_FITNESS
## 0.04 0.03
## NEWS_AND_MAGAZINES PHOTOGRAPHY
## 0.03 0.03
## PRODUCTIVITY COMMUNICATION
## 0.03 0.02
## SHOPPING SOCIAL
## 0.02 0.02
## SPORTS TRAVEL_AND_LOCAL
## 0.02 0.02
## ART_AND_DESIGN AUTO_AND_VEHICLES
## 0.01 0.01
## FOOD_AND_DRINK GAME_ACTION
## 0.01 0.01
## GAME_ARCADE GAME_CASUAL
## 0.01 0.01
## GAME_EDUCATIONAL GAME_PUZZLE
## 0.01 0.01
## GAME_SIMULATION MAPS_AND_NAVIGATION
## 0.01 0.01
## MEDICAL VIDEO_PLAYERS
## 0.01 0.01
## WEATHER
## 0.01 0.00
## Accounting Alfabe �?ren
## 0.00 0.00
## Breaking News Channel 2 News
## 0.00 0.00
## ETEA & MDCAT Islamic Name Boy & Girl+Meaning
## 0.00 0.00
## Mexpost) not notified you follow -
## 0.00 0.00
## Podcasts Romantic Song Music Love Songs
## 0.00 0.00
## Speaker Pro 2019 super loud speaker booster
## 0.00 0.00
## Tour Guide T�rk Alfabesi
## 0.00 0.00
## ) 6
## 0.00 0.00
## BEAUTY COMICS
## 0.00 0.00
## DATING EVENTS
## 0.00 0.00
## GAME_ADVENTURE GAME_BOARD
## 0.00 0.00
## GAME_CARD GAME_CASINO
## 0.00 0.00
## GAME_MUSIC GAME_RACING
## 0.00 0.00
## GAME_ROLE_PLAYING GAME_SPORTS
## 0.00 0.00
## GAME_STRATEGY GAME_TRIVIA
## 0.00 0.00
## GAME_WORD Gate ALARM
## 0.00 0.00
## HOUSE_AND_HOME LIBRARIES_AND_DEMO
## 0.00 0.00
## PARENTING TRAVEL
## 0.00 0.00Too many catergories; grouping them together for a more even spread.
g_apps5 <- g_apps4
g_apps5$Category <- as.character(g_apps5$Category)
g_apps5$Category[g_apps5$Category %in% "BUSINESS"] <- "EDUCATION"
g_apps5$Category[g_apps5$Category %in% "FINANCE"] <- "EDUCATION"
g_apps5$Category[g_apps5$Category %in% "ETEA & MDCAT"] <- "EDUCATION"
g_apps5$Category[g_apps5$Category %in% "PARENTING"] <- "EDUCATION"
g_apps5$Category[g_apps5$Category %in% "BOOKS_AND_REFERENCE"] <- "EDUCATION"
g_apps5$Category[g_apps5$Category %in% "LIBRARIES_AND_DEMO"] <- "EDUCATION"
g_apps5$Category[g_apps5$Category %in% "HEALTH_AND_FITNESS"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "FOOD_AND_DRINK"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "MEDICAL"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "BEAUTY"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "HEALTH"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "NEWS_AND_MAGAZINES"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "SHOPPING"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "TRAVEL_AND_LOCAL"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "ART_AND_DESIGN"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "AUTO_AND_VEHICLES"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "Mexpost)"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "not notified you follow -"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "TÔøΩrk Alfabesi"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "Alfabe ÔøΩ?ren"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% ")"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "6"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "Tour Guide"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "TRAVEL"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "BEAUTY"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "Mexpost)"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "Breaking News"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "Channel 2 News"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "DATING"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "EVENTS"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "SOCIAL"] <- "LIFESTYLE"
g_apps5$Category[g_apps5$Category %in% "PHOTOGRAPHY"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "COMMUNICATION"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "MAPS_AND_NAVIGATION"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "VIDEO_PLAYERS"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "WEATHER"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "HOUSE_AND_HOME"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "VIDEO_PLAYERS"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "Gate ALARM"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "Islamic Name Boy & Girl+Meaning"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "PERSONALIZATION"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "TOOLS"] <- "PRODUCTIVITY"
g_apps5$Category[g_apps5$Category %in% "MUSIC_AND_AUDIO"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "Romantic Song Music Love Songs"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "Speaker Pro 2019"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "super loud speaker booster"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "MUSIC_AND_AUDIO"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "SPORTS"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_ACTION"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_ARCADE"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_CASUAL"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_EDUCATIONAL"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_PUZZLE"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_SIMULATION"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "COMICS"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_ADVENTURE"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_BOARD"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_CARD"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_CASINO"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_MUSIC"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_RACING"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_ROLE_PLAYING"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_SPORTS"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_STRATEGY"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_TRIVIA"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "GAME_WORD"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "Podcasts"] <- "ENTERTAINMENT"
g_apps5$Category[g_apps5$Category %in% "MUSIC"] <- "ENTERTAINMENT"
g_apps5$Category <- as.factor(g_apps5$Category)
ct <- table(g_apps5$Category)
pct <- prop.table(ct)
pct <- round(pct, 2)
pct##
## EDUCATION ENTERTAINMENT LIFESTYLE PRODUCTIVITY
## 0.29 0.25 0.22 0.24par(mfrow=c(1,1))
barplot(pct, main = "Proportion of Apps by Category", col = c("#00DCFF", "#F83648", "#FFD800", "#04F075"), ylim = c(0,0.5), xlab = "Category of App", ylab = "Proportion of Apps")
legend("topright", fill = c("#00DCFF", "#F83648", "#FFD800", "#04F075"), legend = levels(g_apps5$Category))
box()
g_apps6 <- g_apps5
str(g_apps6$Reviews)## num [1:255407] 305034 1207922 1967 389154 2291 ...summary(g_apps6$Reviews)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1 18 101 15246 708 86214292hist(g_apps6$Reviews, breaks = 10, col = "#04F075")
plot(density(g_apps6$Reviews)) # Nowhere near normal distribution
boxplot(g_apps6$Reviews, col = "#00DCFF")
options(scipen = 99)
par(mfrow=c(1,1))
plot(density(log(g_apps6$Reviews)))
hist(log(g_apps6$Reviews), col = "#FFD800", breaks = 100) # Way better, but right skewed a bit
# Removing outliers
log_reviews <- log(g_apps6$Reviews)
revup_limit <- fivenum(log_reviews, na.rm=T)[4]+IQR(log_reviews)*1.5
revup_outliers <- which(log_reviews > revup_limit)
length(revup_outliers) # 2796 outliers## [1] 2796revlow_limit <- fivenum(log_reviews)[2]-IQR(log_reviews)*1.5
revlow_outliers <- which(log_reviews < revlow_limit)
length(revlow_outliers) # 0 outliers## [1] 0g_apps6$Reviews <- log(g_apps6$Reviews) # Using the log transformation, because although it is right skewed, it's more normally distruted
g_apps7 <- g_apps6[-revup_outliers,]
plot(density(g_apps7$Reviews), main = "Density Plot log Reviews", lwd = 3, xlab = "Log of Reviews", col="#00DCFF")
#-------------- Installs ---------------#
summary(g_apps7$Installs)## 0 1 10 100 1000 10000
## 45 426 4069 16533 45961 58598
## 100000 1000000 10000000 100000000 1000000000 5
## 36736 12599 1221 22 0 640
## 50 500 5000 50000 500000 5000000
## 3486 12693 25268 22184 9685 2414
## 50000000 500000000 5000000000
## 26 5 0summary(as.numeric(as.character(g_apps7$Installs)))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 1000 10000 210881 50000 500000000g_apps7$Installs <- as.numeric(as.character(g_apps7$Installs))
hist(g_apps7$Installs, col = "#00DCFF", breaks = 1000)
plot(density(g_apps7$Installs), col = "#00DCFF", lwd=3) 
# Why is the data so skewed?
toohigh <- which(g_apps7$Installs %in% 500000000)
length(toohigh) # Only 5 apps have up to 5 million installs## [1] 5boxplot(g_apps7$Installs)
# Let me try data transformation to see if I can find a more normal distribution.
plot(density(log(g_apps7$Installs)), col = "#04F075", lwd = 3)
plot(density(sqrt(g_apps7$Installs)), col = "#04F075", lwd = 3)
plot(density(g_apps7$Installs^(1/3)), col = "#04F075", lwd = 3) # None of these data transformations achieve normal distribution.
# As a numeric variable, Installs is extremely skewed so I will convert it to a factor with 5 groups.
g_apps7$Installs <- as.character(g_apps7$Installs)
g_apps7$Installs[g_apps7$Installs %in% c(0,1,5,10,50,100,500)] <- "0-500"
g_apps7$Installs[g_apps7$Installs %in% c(1000,5000)] <- "1000-10000"
g_apps7$Installs[g_apps7$Installs %in% c(10000,50000)] <- "10000-100000"
g_apps7$Installs[g_apps7$Installs %in% c(100000,500000)] <- "100000-1000000"
g_apps7$Installs[g_apps7$Installs %in% c(1000000,5000000,10000000,50000000, 100000000,500000000)] <- "1000000+"
g_apps7$Installs <- as.factor(g_apps7$Installs)
summary(g_apps7$Installs)## 0-500 1000-10000 10000-100000 100000-1000000 1000000+
## 37892 71229 80782 46421 16287install_tab <- table(g_apps7$Installs)
install_ptab <- round(prop.table(install_tab), 2)
install_ptab##
## 0-500 1000-10000 10000-100000 100000-1000000 1000000+
## 0.15 0.28 0.32 0.18 0.06barplot(install_ptab, main = "Installs", xlab = "Number of Installs", ylab = "Proportion of Data", ylim = c(0,0.4), col = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"))
legend("topright", fill = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"), legend = c("< 1k Installs", "1k-9.9k Installs", "10k-99k Installs", "100k-999k", "1M+ Installs"))
box()
# -------- Size ----------#
g_apps8 <- g_apps7
summary(g_apps8$Size) # This variable cannot be numeric since "Varies with device" is a value## Varies with device 11000000 12000000
## 10671 6927 6061
## 13000000 14000000 15000000
## 5307 4966 4908
## 16000000 10000000 17000000
## 4315 4236 3567
## 18000000 19000000 20000000
## 3444 3364 3074
## 21000000 23000000 22000000
## 2788 2606 2572
## 24000000 3800000 3400000
## 2556 2517 2501
## 3300000 25000000 3600000
## 2493 2492 2473
## 3200000 3700000 3900000
## 2456 2427 2368
## 3500000 2900000 4000000
## 2363 2305 2279
## 3100000 2800000 26000000
## 2274 2240 2229
## 3000000 4100000 2600000
## 2212 2107 2100
## 4500000 4300000 2700000
## 2077 2067 2014
## 4900000 27000000 4200000
## 2013 1968 1963
## 2300000 2500000 2400000
## 1925 1916 1912
## 4400000 4600000 4700000
## 1874 1801 1797
## 4800000 5000000 5100000
## 1794 1778 1778
## 28000000 2200000 5200000
## 1776 1726 1701
## 30000000 5800000 29000000
## 1686 1670 1612
## 5300000 2000000 6000000
## 1606 1605 1598
## 31000000 5500000 5600000
## 1594 1536 1519
## 5400000 5900000 5700000
## 1511 1490 1480
## 2100000 32000000 6100000
## 1464 1433 1324
## 6400000 6200000 6500000
## 1314 1306 1285
## 1900000 6300000 33000000
## 1284 1280 1277
## 36000000 34000000 1800000
## 1269 1256 1247
## 6600000 35000000 7400000
## 1214 1213 1202
## 1700000 6900000 7200000
## 1184 1168 1156
## 37000000 7000000 6700000
## 1141 1136 1124
## 7300000 7100000 6800000
## 1116 1111 1074
## 7500000 7600000 1500000
## 1070 1067 1052
## 38000000 7900000 7700000
## 1018 1015 1014
## 8300000 1400000 8200000
## 1011 1005 1003
## 1600000 7800000 39000000
## 997 974 964
## (Other)
## 46858# I'll add a new variable for size groupings
vwd <- which(g_apps8$Size == "Varies with device")
g_apps8.1 <- g_apps8[-vwd,]
summary(g_apps8.1$Size)## 11000000 12000000 13000000 14000000 15000000 16000000 10000000 17000000
## 6927 6061 5307 4966 4908 4315 4236 3567
## 18000000 19000000 20000000 21000000 23000000 22000000 24000000 3800000
## 3444 3364 3074 2788 2606 2572 2556 2517
## 3400000 3300000 25000000 3600000 3200000 3700000 3900000 3500000
## 2501 2493 2492 2473 2456 2427 2368 2363
## 2900000 4000000 3100000 2800000 26000000 3000000 4100000 2600000
## 2305 2279 2274 2240 2229 2212 2107 2100
## 4500000 4300000 2700000 4900000 27000000 4200000 2300000 2500000
## 2077 2067 2014 2013 1968 1963 1925 1916
## 2400000 4400000 4600000 4700000 4800000 5000000 5100000 28000000
## 1912 1874 1801 1797 1794 1778 1778 1776
## 2200000 5200000 30000000 5800000 29000000 5300000 2000000 6000000
## 1726 1701 1686 1670 1612 1606 1605 1598
## 31000000 5500000 5600000 5400000 5900000 5700000 2100000 32000000
## 1594 1536 1519 1511 1490 1480 1464 1433
## 6100000 6400000 6200000 6500000 1900000 6300000 33000000 36000000
## 1324 1314 1306 1285 1284 1280 1277 1269
## 34000000 1800000 6600000 35000000 7400000 1700000 6900000 7200000
## 1256 1247 1214 1213 1202 1184 1168 1156
## 37000000 7000000 6700000 7300000 7100000 6800000 7500000 7600000
## 1141 1136 1124 1116 1111 1074 1070 1067
## 1500000 38000000 7900000 7700000 8300000 1400000 8200000 1600000
## 1052 1018 1015 1014 1011 1005 1003 997
## 7800000 39000000 8000000 (Other)
## 974 964 948 45910g_apps8.1$Size <- as.numeric(as.character(g_apps8.1$Size))
str(g_apps8.1$Size)## num [1:241940] 1400000 23000000 4100000 39000000 8100000 19000000 30000000 11000000 11000000 23000000 ...fivenum(g_apps8.1$Size) # minimum value is 3.1 so I'll set "Varies with device to 1## [1] 3.1 4000000.0 8300000.0 19000000.0 334000000.0g_apps8$Size <- as.character(g_apps8$Size)
g_apps8$Size[g_apps8$Size == "Varies with device"] <- 1
g_apps8$Size <- as.numeric(as.character(g_apps8$Size))
g_apps8$Size.Groups <- cut(g_apps8$Size, breaks = c(0,3,4000000,8300000,19000000,334000000), labels = c("Varies with device", "0-4M", "4M-8.3M", "8.3M-19M", "19M-334M"))
summary(g_apps8$Size.Groups)## Varies with device 0-4M 4M-8.3M
## 10671 60671 61008
## 8.3M-19M 19M-334M
## 60798 59463sgtab <- table(g_apps8$Size.Groups)
psgtab <- prop.table(sgtab)
psgtab # groupings look proportionate aside from group 5 which is "Varies by device"##
## Varies with device 0-4M 4M-8.3M
## 0.04224282 0.24017561 0.24150967
## 8.3M-19M 19M-334M
## 0.24067836 0.23539355barplot(psgtab, main = "App Size Groupings", col = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"), xlab = "Size Group", ylab = "Proportion", ylim = c(0,0.3))
legend("topleft", fill = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"), legend = levels(g_apps8$Size.Groups))
g_apps9 <- g_apps8
g_apps9$Price <- as.numeric(as.character(g_apps9$Price))
summary(g_apps9$Price)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.0000 0.0000 0.2309 0.0000 399.9900pt <- table(as.factor(g_apps9$Price))
ppt <- prop.table(pt)
ppt # over 95% of apps in this dataset cost $0 to download (Free), I'll convert to a factor##
## 0 0.67 0.99 1 1.01
## 0.955876822466 0.000003958656 0.008685290823 0.000178139511 0.000011875967
## 1.02 1.03 1.04 1.05 1.06
## 0.000003958656 0.000007917312 0.000003958656 0.000011875967 0.000003958656
## 1.07 1.08 1.09 1.1 1.11
## 0.000003958656 0.000011875967 0.000019793279 0.000015834623 0.000015834623
## 1.12 1.13 1.17 1.18 1.19
## 0.000003958656 0.000003958656 0.000007917312 0.000003958656 0.000059379837
## 1.2 1.21 1.22 1.23 1.25
## 0.000035627902 0.000003958656 0.000003958656 0.000003958656 0.000019793279
## 1.26 1.27 1.28 1.29 1.3
## 0.000007917312 0.000003958656 0.000003958656 0.000063338493 0.000015834623
## 1.32 1.33 1.34 1.35 1.36
## 0.000011875967 0.000015834623 0.000015834623 0.000007917312 0.000011875967
## 1.37 1.38 1.39 1.4 1.42
## 0.000003958656 0.000007917312 0.000015834623 0.000007917312 0.000007917312
## 1.43 1.44 1.45 1.48 1.49
## 0.000003958656 0.000003958656 0.000019793279 0.000011875967 0.002858149487
## 1.5 1.51 1.52 1.53 1.55
## 0.000051462525 0.000007917312 0.000003958656 0.000003958656 0.000003958656
## 1.56 1.58 1.59 1.61 1.62
## 0.000003958656 0.000003958656 0.000039586558 0.000007917312 0.000007917312
## 1.66 1.67 1.68 1.69 1.7
## 0.000003958656 0.000003958656 0.000011875967 0.000011875967 0.000023751935
## 1.72 1.74 1.75 1.77 1.78
## 0.000003958656 0.000007917312 0.000031669246 0.000011875967 0.000007917312
## 1.79 1.8 1.81 1.82 1.84
## 0.000019793279 0.000023751935 0.000011875967 0.000007917312 0.000003958656
## 1.85 1.86 1.88 1.89 1.9
## 0.000007917312 0.000007917312 0.000003958656 0.000007917312 0.000011875967
## 1.92 1.93 1.94 1.95 1.96
## 0.000007917312 0.000003958656 0.000003958656 0.000035627902 0.000015834623
## 1.97 1.98 1.99 2 2.02
## 0.000019793279 0.000003958656 0.005937983698 0.000162304888 0.000003958656
## 2.03 2.04 2.09 2.1 2.13
## 0.000011875967 0.000007917312 0.000015834623 0.000007917312 0.000003958656
## 2.15 2.19 2.2 2.25 2.27
## 0.000003958656 0.000003958656 0.000007917312 0.000007917312 0.000003958656
## 2.28 2.29 2.3 2.31 2.32
## 0.000007917312 0.000015834623 0.000003958656 0.000007917312 0.000007917312
## 2.33 2.35 2.36 2.37 2.39
## 0.000003958656 0.000007917312 0.000003958656 0.000003958656 0.000011875967
## 2.4 2.41 2.42 2.43 2.45
## 0.000007917312 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 2.46 2.48 2.49 2.5 2.51
## 0.000015834623 0.000011875967 0.001983286555 0.000039586558 0.000003958656
## 2.52 2.54 2.55 2.57 2.59
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000027710591
## 2.6 2.64 2.65 2.66 2.67
## 0.000003958656 0.000003958656 0.000007917312 0.000003958656 0.000015834623
## 2.69 2.71 2.73 2.74 2.77
## 0.000007917312 0.000007917312 0.000003958656 0.000003958656 0.000011875967
## 2.79 2.8 2.82 2.84 2.85
## 0.000015834623 0.000003958656 0.000003958656 0.000007917312 0.000011875967
## 2.86 2.89 2.9 2.93 2.94
## 0.000003958656 0.000015834623 0.000031669246 0.000011875967 0.000003958656
## 2.95 2.98 2.99 3 3.01
## 0.000003958656 0.000003958656 0.005205632375 0.000083131772 0.000003958656
## 3.03 3.06 3.08 3.09 3.1
## 0.000003958656 0.000003958656 0.000023751935 0.000003958656 0.000003958656
## 3.11 3.14 3.16 3.22 3.24
## 0.000007917312 0.000003958656 0.000003958656 0.000007917312 0.000003958656
## 3.25 3.26 3.27 3.28 3.29
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000007917312
## 3.32 3.33 3.36 3.38 3.39
## 0.000007917312 0.000003958656 0.000003958656 0.000007917312 0.000007917312
## 3.4 3.41 3.42 3.43 3.49
## 0.000003958656 0.000003958656 0.000007917312 0.000003958656 0.001302397758
## 3.5 3.55 3.58 3.59 3.63
## 0.000023751935 0.000011875967 0.000003958656 0.000007917312 0.000003958656
## 3.65 3.72 3.75 3.77 3.78
## 0.000003958656 0.000003958656 0.000015834623 0.000003958656 0.000003958656
## 3.8 3.81 3.82 3.83 3.84
## 0.000003958656 0.000007917312 0.000007917312 0.000007917312 0.000003958656
## 3.85 3.89 3.9 3.91 3.93
## 0.000003958656 0.000003958656 0.000019793279 0.000003958656 0.000003958656
## 3.95 3.97 3.98 3.99 4
## 0.000027710591 0.000003958656 0.000007917312 0.002945239914 0.000031669246
## 4.03 4.04 4.06 4.14 4.17
## 0.000003958656 0.000011875967 0.000003958656 0.000003958656 0.000003958656
## 4.19 4.2 4.25 4.26 4.29
## 0.000003958656 0.000007917312 0.000011875967 0.000003958656 0.000007917312
## 4.3 4.31 4.34 4.35 4.38
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 4.39 4.4 4.41 4.42 4.44
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 4.48 4.49 4.5 4.53 4.54
## 0.000003958656 0.000977787982 0.000007917312 0.000003958656 0.000003958656
## 4.56 4.57 4.62 4.63 4.64
## 0.000003958656 0.000003958656 0.000003958656 0.000007917312 0.000003958656
## 4.69 4.71 4.72 4.73 4.74
## 0.000011875967 0.000003958656 0.000007917312 0.000003958656 0.000003958656
## 4.77 4.8 4.82 4.85 4.88
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 4.89 4.9 4.95 4.97 4.98
## 0.000011875967 0.000015834623 0.000019793279 0.000003958656 0.000003958656
## 4.99 5 5.01 5.29 5.3
## 0.003388609364 0.000047503870 0.000003958656 0.000007917312 0.000003958656
## 5.33 5.36 5.38 5.4 5.48
## 0.000007917312 0.000003958656 0.000003958656 0.000003958656 0.000015834623
## 5.49 5.5 5.55 5.57 5.69
## 0.000577963747 0.000003958656 0.000007917312 0.000003958656 0.000003958656
## 5.72 5.74 5.76 5.78 5.79
## 0.000003958656 0.000007917312 0.000003958656 0.000003958656 0.000003958656
## 5.9 5.95 5.96 5.98 5.99
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000866945620
## 6 6.04 6.14 6.15 6.16
## 0.000023751935 0.000003958656 0.000007917312 0.000003958656 0.000003958656
## 6.21 6.27 6.28 6.29 6.3
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 6.49 6.52 6.54 6.57 6.58
## 0.000249395315 0.000003958656 0.000015834623 0.000011875967 0.000003958656
## 6.59 6.64 6.69 6.7 6.71
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 6.73 6.84 6.85 6.87 6.9
## 0.000003958656 0.000003958656 0.000007917312 0.000003958656 0.000003958656
## 6.98 6.99 7 7.03 7.12
## 0.000007917312 0.000653178207 0.000007917312 0.000003958656 0.000003958656
## 7.14 7.23 7.49 7.53 7.55
## 0.000003958656 0.000003958656 0.000253353971 0.000003958656 0.000003958656
## 7.56 7.64 7.68 7.73 7.74
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000007917312
## 7.85 7.89 7.99 8 8.34
## 0.000003958656 0.000011875967 0.000676930142 0.000007917312 0.000003958656
## 8.35 8.43 8.47 8.49 8.66
## 0.000003958656 0.000003958656 0.000003958656 0.000134594297 0.000003958656
## 8.69 8.75 8.8 8.9 8.92
## 0.000003958656 0.000003958656 0.000007917312 0.000011875967 0.000003958656
## 8.99 9 9.13 9.17 9.49
## 0.000312733808 0.000003958656 0.000003958656 0.000003958656 0.000186056823
## 9.71 9.76 9.79 9.8 9.9
## 0.000003958656 0.000003958656 0.000003958656 0.000007917312 0.000011875967
## 9.95 9.99 10 10.14 10.15
## 0.000015834623 0.001053002442 0.000015834623 0.000003958656 0.000003958656
## 10.25 10.49 10.7 10.75 10.99
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000178139511
## 11 11.07 11.1 11.41 11.99
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000174180855
## 12 12.49 12.62 12.93 12.99
## 0.000011875967 0.000011875967 0.000003958656 0.000003958656 0.000193974134
## 13.37 13.46 13.48 13.52 13.61
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 13.99 14.01 14.5 14.73 14.93
## 0.000106883707 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 14.99 15 15.01 15.68 15.99
## 0.000261271283 0.000007917312 0.000003958656 0.000003958656 0.000114801018
## 16.17 16.99 17.92 17.98 17.99
## 0.000003958656 0.000067297149 0.000003958656 0.000003958656 0.000071255804
## 18 18.6 18.99 19.01 19.49
## 0.000003958656 0.000003958656 0.000059379837 0.000003958656 0.000003958656
## 19.5 19.7 19.9 19.95 19.98
## 0.000003958656 0.000003958656 0.000007917312 0.000003958656 0.000003958656
## 19.99 20.99 21 21.99 22.22
## 0.000197932790 0.000039586558 0.000003958656 0.000055421181 0.000003958656
## 22.99 23.32 23.45 23.92 23.99
## 0.000055421181 0.000003958656 0.000003958656 0.000003958656 0.000023751935
## 24.46 24.64 24.95 24.99 25
## 0.000003958656 0.000003958656 0.000003958656 0.000174180855 0.000003958656
## 25.99 26.9 26.99 27.01 27.47
## 0.000003958656 0.000003958656 0.000031669246 0.000003958656 0.000003958656
## 27.5 27.99 28.99 29.95 29.99
## 0.000007917312 0.000039586558 0.000027710591 0.000007917312 0.000150428920
## 30.99 31.99 32.99 33.99 34
## 0.000003958656 0.000007917312 0.000039586558 0.000011875967 0.000003958656
## 34.99 35 35.99 37.84 37.99
## 0.000023751935 0.000003958656 0.000023751935 0.000003958656 0.000015834623
## 38.99 39.8 39.99 40.99 42.99
## 0.000031669246 0.000003958656 0.000023751935 0.000007917312 0.000003958656
## 43.99 44.99 45.99 46.99 49
## 0.000003958656 0.000003958656 0.000003958656 0.000007917312 0.000003958656
## 49.95 49.99 50 52.25 53.47
## 0.000003958656 0.000031669246 0.000003958656 0.000003958656 0.000003958656
## 54.99 59.99 64.99 69 69.99
## 0.000047503870 0.000007917312 0.000015834623 0.000003958656 0.000027710591
## 74.99 79.99 81.18 84.99 89.99
## 0.000011875967 0.000039586558 0.000003958656 0.000007917312 0.000003958656
## 94.99 99 99.9 99.95 99.99
## 0.000007917312 0.000003958656 0.000007917312 0.000003958656 0.000003958656
## 100 104.99 109.99 114.99 119.99
## 0.000003958656 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 124.99 129.99 134.99 140 184.99
## 0.000007917312 0.000007917312 0.000003958656 0.000003958656 0.000007917312
## 199.99 234.99 244.99 289.99 299.9
## 0.000011875967 0.000003958656 0.000003958656 0.000003958656 0.000003958656
## 299.99 309.99 369.99 374.99 379.99
## 0.000007917312 0.000003958656 0.000007917312 0.000003958656 0.000007917312
## 389.99 399.99
## 0.000003958656 0.000019793279g_apps9$Price <- as.character(g_apps9$Price)
g_apps9$Price[g_apps9$Price %in% "0"] <- "Free"
g_apps9$Price[g_apps9$Price != "Free"] <- "Paid"
ptab <- table(g_apps9$Price)
pptab <- prop.table(ptab)
pptab##
## Free Paid
## 0.95587682 0.04412318g_apps9$Price <- as.factor(g_apps9$Price)
summary(g_apps9$Price) # 4.4% of apps cost money## Free Paid
## 241465 11146barplot(ptab, main = "Price of Apps", col = c("#00DCFF", "#F83648"), ylab = "Number of apps", xlab = "Type of App", ylim = c(0,250000))
legend("topright", fill = c("#00DCFF", "#F83648"), legend = levels(g_apps9$Price))
g_apps10 <- g_apps9
summary(g_apps10$Content.Rating) ## $0.99 $2.49 0 100,000+
## 0 0 0 0
## 17M 3702 Adults only 18+ Everyone
## 0 0 11 228790
## Everyone 10+ Mature 17+ Teen Unrated
## 4337 3234 16206 33g_apps10$Content.Rating <- as.factor(g_apps10$Content.Rating)
crtab <- table(g_apps10$Content.Rating)
pcrtab <- prop.table(crtab)
pcrtab ##
## $0.99 $2.49 0 100,000+
## 0.00000000000 0.00000000000 0.00000000000 0.00000000000
## 17M 3702 Adults only 18+ Everyone
## 0.00000000000 0.00000000000 0.00004354521 0.90570086022
## Everyone 10+ Mature 17+ Teen Unrated
## 0.01716869020 0.01280229285 0.06415397588 0.00013063564pie3D(crtab, explode = 0.1, main = "App Content Ratings", theta = 1.5, labels = levels(g_apps10$Content.Rating), col = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"))
# The groups are very disproportionate, lets group some together
g_apps10$Content.Rating <- as.character(g_apps10$Content.Rating)
g_apps10$Content.Rating[g_apps10$Content.Rating == "Everyone 10+"] <- "Mature"
g_apps10$Content.Rating[g_apps10$Content.Rating == "Adults only 18+"] <- "Mature"
g_apps10$Content.Rating[g_apps10$Content.Rating == "Teen"] <- "Mature"
g_apps10$Content.Rating[g_apps10$Content.Rating == "Unrated"] <- "Mature"
g_apps10$Content.Rating[g_apps10$Content.Rating == "Mature 17+"] <- "Mature"
g_apps10$Content.Rating <- as.factor(g_apps10$Content.Rating)
summary(g_apps10$Content.Rating)## Everyone Mature
## 228790 23821new_crtab <- table(g_apps10$Content.Rating)
new_pcrtab <- prop.table(new_crtab)
new_pcrtab##
## Everyone Mature
## 0.90570086 0.09429914pie3D(new_pcrtab, explode = 0.1, main = "App Content Ratings", theta = 1.5, col = c("#00DCFF", "#F83648"))
legend("topright", legend = levels(g_apps10$Content.Rating), fill = c("#00DCFF", "#F83648"))
g_apps11 <- g_apps10[,-c(10,11)] # Removed last and minimum versions because I won't be using those variablesBivariate Analysis
table(is.na(g_apps11$Rating)) # No missing values##
## FALSE
## 252611plot(g_apps11$Rating~g_apps11$Reviews, col = "black", main="Reviews vs App Ratings",
xlab = "Log Reviews",
ylab = "Ratings", pch=20,
xlim = c(0, 25))
abline(lm(g_apps11$Rating~g_apps11$Reviews), col="#F83648", lwd=2.5)
lines(lowess(g_apps11$Rating~g_apps11$Reviews), col="#00DCFF", lwd=2.5)
library(corrplot)
cor(g_apps11$Rating, g_apps11$Reviews) # Very weak negative coorelation ## [1] -0.1726915cormat <- cor(g_apps11[,c(3,4)])
corrplot(cormat, method = "circle", addCoef.col = "red")
cor.test(g_apps11$Rating, g_apps11$Reviews)##
## Pearson's product-moment correlation
##
## data: g_apps11$Rating and g_apps11$Reviews
## t = -88.119, df = 252609, p-value < 0.00000000000000022
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.1764723 -0.1689057
## sample estimates:
## cor
## -0.1726915The results from the correlation test show that we can reject the Null hypothesis. There is a correlation between Ratings and Reviews, however the correlation is a very weak, negative one at -0.17.
This also tells me that I can include both ratings and reviews in my regression model since multicollinearity is not an issue here.
Now I’ll look at how each variable affects the target variable, Installs.
install_size <- table(g_apps11$Size.Groups, g_apps11$Installs)
pinstall_size <- prop.table(install_size)
pinstall_size <- round(pinstall_size,2)
addmargins(pinstall_size,c(1,2))##
## 0-500 1000-10000 10000-100000 100000-1000000 1000000+
## Varies with device 0.00 0.01 0.01 0.01 0.01
## 0-4M 0.04 0.07 0.08 0.04 0.01
## 4M-8.3M 0.04 0.07 0.08 0.04 0.01
## 8.3M-19M 0.04 0.07 0.08 0.04 0.01
## 19M-334M 0.03 0.06 0.07 0.05 0.02
## Sum 0.15 0.28 0.32 0.18 0.06
##
## Sum
## Varies with device 0.04
## 0-4M 0.24
## 4M-8.3M 0.24
## 8.3M-19M 0.24
## 19M-334M 0.23
## Sum 0.99ptab_size <- prop.table(install_size, margin = 2)
barplot(ptab_size, col = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"), main = "Installs vs Size", xlab = "Number of Installs", ylab = "Proportion")
legend("topright", fill = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444"), legend = levels(g_apps11$Size.Groups))
chisq.test(pinstall_size)## Warning in chisq.test(pinstall_size): Chi-squared approximation may be
## incorrect##
## Pearson's Chi-squared test
##
## data: pinstall_size
## X-squared = 0.043817, df = 16, p-value = 1The results of the chi-squared test are higher that 0.05 so we will accept the null hypothesis. It seems that size of app has no effect on the number of installs an app receives. This may actually be true if we assume that many consumers do not look at app size before downloading an app. However, the small amount of data we have on “varies with device” could be the reason the p-value is a 1. More data would be needed to conduct a more succesful test.
g_apps11 %>% group_by(Installs) %>% summarise(avg = mean(Rating), median = median(Rating), std = sd(Rating))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 5 x 4
## Installs avg median std
## <fct> <dbl> <dbl> <dbl>
## 1 0-500 4.65 4.97 0.473
## 2 1000-10000 4.35 4.43 0.464
## 3 10000-100000 4.28 4.37 0.403
## 4 100000-1000000 4.26 4.32 0.356
## 5 1000000+ 4.25 4.29 0.312boxplot(Rating~Installs, data = g_apps11, main="Boxplot of Ratings by Installs", xlab = "Install Group",
col = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444")) # Looks like apps with fewer intalls have a higher rating on average
rat_install.aov <- aov(Rating~Installs, data = g_apps11)
summary(rat_install.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Installs 4 4352 1087.9 6191 <0.0000000000000002 ***
## Residuals 252606 44389 0.2
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(rat_install.aov) # For coomparison of levels## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Rating ~ Installs, data = g_apps11)
##
## $Installs
## diff lwr upr
## 1000-10000-0-500 -0.300102885 -0.30737361 -0.292832160
## 10000-100000-0-500 -0.371134212 -0.37825409 -0.364014336
## 100000-1000000-0-500 -0.390823127 -0.39873979 -0.382906467
## 1000000+-0-500 -0.395944779 -0.40665866 -0.385230895
## 10000-100000-1000-10000 -0.071031327 -0.07690862 -0.065154031
## 100000-1000000-1000-10000 -0.090720242 -0.09754105 -0.083899431
## 1000000+-1000-10000 -0.095841894 -0.10577352 -0.085910264
## 100000-1000000-10000-100000 -0.019688915 -0.02634869 -0.013029135
## 1000000+-10000-100000 -0.024810567 -0.03463230 -0.014988833
## 1000000+-100000-1000000 -0.005121652 -0.01553546 0.005292153
## p adj
## 1000-10000-0-500 0.0000000
## 10000-100000-0-500 0.0000000
## 100000-1000000-0-500 0.0000000
## 1000000+-0-500 0.0000000
## 10000-100000-1000-10000 0.0000000
## 100000-1000000-1000-10000 0.0000000
## 1000000+-1000-10000 0.0000000
## 100000-1000000-10000-100000 0.0000000
## 1000000+-10000-100000 0.0000000
## 1000000+-100000-1000000 0.6651233#verify ANOVA assumptions with diagnostic plots
plot(rat_install.aov)
Here we can see that apps with fewer installs have higher ratings on average. This makes sense because apps with a high number of installs would have a large number of ratings. Each rating would carry less weight and at the same time a large number of people rating an app would likely introduce a wider range of ratings, driving the average rating down over time.
The p-value for the ANOVA test was low enough to reject the null hypothesis. I also used diagnostics plots to verify that the ANOVA assumptions were correct. The data does have some outliers but in general the plots look good. More specifically, the Residuals vs. Fitted plot shows that there is homogeniety among variances as there is no relationship between the residuals of each group. The Normal Q-Q plot tells us that residuals are normally distributed.
g_apps11 %>% group_by(Installs) %>% summarise(avg = mean(Reviews), median = median(Reviews), std = sd(Reviews))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 5 x 4
## Installs avg median std
## <fct> <dbl> <dbl> <dbl>
## 1 0-500 1.49 1.39 1.08
## 2 1000-10000 3.17 3.18 1.14
## 3 10000-100000 5.19 5.15 1.15
## 4 100000-1000000 7.41 7.38 1.18
## 5 1000000+ 9.91 9.94 1.16boxplot(Reviews~Installs, data = g_apps11, main="Boxplot of Reviews by Installs",
col = c("#00DCFF", "#F83648", "#FFD800", "#04F075", "#444444")) # Looks fairly equaly, productivity has a slightly less rating.
rev_installs.aov <- aov(Reviews~Installs, data = g_apps11)
summary(rev_installs.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Installs 4 1357431 339358 260055 <0.0000000000000002 ***
## Residuals 252606 329638 1
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(rev_installs.aov) # For coomparison of levels## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Reviews ~ Installs, data = g_apps11)
##
## $Installs
## diff lwr upr p adj
## 1000-10000-0-500 1.687458 1.667645 1.707272 0
## 10000-100000-0-500 3.700072 3.680670 3.719474 0
## 100000-1000000-0-500 5.921287 5.899714 5.942861 0
## 1000000+-0-500 8.424466 8.395270 8.453662 0
## 10000-100000-1000-10000 2.012613 1.996597 2.028629 0
## 100000-1000000-1000-10000 4.233829 4.215242 4.252416 0
## 1000000+-1000-10000 6.737008 6.709943 6.764072 0
## 100000-1000000-10000-100000 2.221216 2.203067 2.239364 0
## 1000000+-10000-100000 4.724394 4.697629 4.751159 0
## 1000000+-100000-1000000 2.503179 2.474800 2.531557 0#verify ANOVA assumptions with diagnostic plots
plot(rev_installs.aov) # we have outliers
As expected, the apps with over 1 million installs have the highest number of reviews on average and apps with fewer than 1,000 installs have the lowest number of reviews. The p-value for the ANOVA test is low enough to make the assumption that these results are correct. Installs and Reviews have a positive relationship with each other. Diagnostic plots look good as well.
ptab <- table(g_apps11$Price, g_apps11$Installs)
pptab <- prop.table(ptab)
pptab <- round(pptab, 2)
addmargins(pptab, c(1,2))##
## 0-500 1000-10000 10000-100000 100000-1000000 1000000+ Sum
## Free 0.13 0.27 0.31 0.18 0.06 0.95
## Paid 0.02 0.01 0.01 0.00 0.00 0.04
## Sum 0.15 0.28 0.32 0.18 0.06 0.99ptab_price <- prop.table(ptab, margin = 2)
barplot(ptab_price, col = c("#00DCFF", "#F83648"), main = "Installs by Price Group", xlab = "Number of Installs", ylab = "Proportion of Apps")
legend("topright", legend = levels(g_apps11$Price), fill = c("#00DCFF", "#F83648")) # disproportionate so of course we expect this
chisq.test(pptab)## Warning in chisq.test(pptab): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: pptab
## X-squared = 0.044366, df = 4, p-value = 0.9998The p-value for the chi-squared test is 0.99 which is high enough to reject the null. This may be due to the disproportionate amount of data available on the price of apps in the dataset. I will not make any conclusions about Installs compared to the Price of an app.
crtab <- table(g_apps11$Content.Rating, g_apps11$Installs)
crtab <- prop.table(crtab)
pcrtab <- round(pptab, 2)
addmargins(pcrtab, c(1,2))##
## 0-500 1000-10000 10000-100000 100000-1000000 1000000+ Sum
## Free 0.13 0.27 0.31 0.18 0.06 0.95
## Paid 0.02 0.01 0.01 0.00 0.00 0.04
## Sum 0.15 0.28 0.32 0.18 0.06 0.99ptab_cr <- prop.table(crtab, margin = 2)
barplot(ptab_cr, col = c("#00DCFF", "#F83648"), main = "Installs by Content rating", xlab = "Number of Installs", ylab = "Proportion of Apps")
legend("topright", legend = levels(g_apps11$Content.Rating), fill = c("#00DCFF", "#F83648")) # disproportionate so of course we expect this
chisq.test(pcrtab)## Warning in chisq.test(pcrtab): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: pcrtab
## X-squared = 0.044366, df = 4, p-value = 0.9998The p-value for the chi-squared test is 0.99 which is high enough to reject the null. This may be due to the disproportionate amount of data available on content rating in the dataset. I will not make any conclusions about Installs compared to the Content Rating of an app.
cattab <- table(g_apps11$Category, g_apps11$Installs)
pcattab <- prop.table(cattab)
pcattab <- round(pcattab, 2)
addmargins(pcattab, c(1,2))##
## 0-500 1000-10000 10000-100000 100000-1000000 1000000+ Sum
## EDUCATION 0.05 0.09 0.10 0.04 0.01 0.29
## ENTERTAINMENT 0.04 0.06 0.08 0.05 0.03 0.26
## LIFESTYLE 0.04 0.07 0.07 0.04 0.01 0.23
## PRODUCTIVITY 0.03 0.06 0.07 0.05 0.02 0.23
## Sum 0.16 0.28 0.32 0.18 0.07 1.01ptab_cat <- prop.table(cattab, margin = 2)
barplot(ptab_cat, col = c("#00DCFF", "#F83648", "#FFD800", "#04F075"), main = "Installs by Category", xlab = "Number of Installs", ylab = "Proportion of Apps")
legend("topright", legend = levels(g_apps11$Category), fill = c("#00DCFF", "#F83648", "#FFD800", "#04F075")) # disproportionate so of course we expect this
chisq.test(pcattab)## Warning in chisq.test(pcattab): Chi-squared approximation may be incorrect##
## Pearson's Chi-squared test
##
## data: pcattab
## X-squared = 0.028116, df = 12, p-value = 1The p-value for the chi-squared test is 1. It seems that Category has no effect on the number of Installs an app receives.
Hypothesis Testing
# Hypothesis 1: Education apps will have higher ratings that all other apps on average.
g_apps11 %>% group_by(Category) %>% summarise(avg = mean(Rating), median = median(Rating), std = sd(Rating))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 4 x 4
## Category avg median std
## <fct> <dbl> <dbl> <dbl>
## 1 EDUCATION 4.39 4.47 0.440
## 2 ENTERTAINMENT 4.37 4.42 0.412
## 3 LIFESTYLE 4.34 4.40 0.467
## 4 PRODUCTIVITY 4.28 4.33 0.431boxplot(Rating~Category, data = g_apps11, main="Boxplot of Ratings by Installs",
col = c("#00DCFF", "#F83648", "#FFD800", "#04F075")) # Looks fairly equaly, productivity has a slightly less rating.
rat_category.aov <- aov(Rating~Category, data = g_apps11)
summary(rat_category.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Category 3 477 159.01 832.3 <0.0000000000000002 ***
## Residuals 252607 48264 0.19
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(rat_category.aov) # For coomparison of levels## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Rating ~ Category, data = g_apps11)
##
## $Category
## diff lwr upr p adj
## ENTERTAINMENT-EDUCATION -0.02201544 -0.02811043 -0.01592046 0
## LIFESTYLE-EDUCATION -0.05476119 -0.06104986 -0.04847251 0
## PRODUCTIVITY-EDUCATION -0.11474899 -0.12094437 -0.10855361 0
## LIFESTYLE-ENTERTAINMENT -0.03274574 -0.03924470 -0.02624679 0
## PRODUCTIVITY-ENTERTAINMENT -0.09273355 -0.09914227 -0.08632482 0
## PRODUCTIVITY-LIFESTYLE -0.05998780 -0.06658101 -0.05339460 0#verify ANOVA assumptions with diagnostic plots
plot(rat_category.aov) # we have outliers
The results show that we can reject the null hypothesis. The Tukey pairwise test shows that there is a significant difference between the means of each category and Education apps actually do have higher ratings on average. Productivity apps have the lowest average rating of the 4 groups. Test results are significant.
I also used diagnostics plots to verify that the ANOVA assumptions were correct. The data does have some outliers but in general the plots look good. More specifically, the Residuals vs. Fitted plot shows that there is homogeniety among variances as there is no relationship between the residuals of each group. The Normal Q-Q plot tells us that residuals are normally distributed.
# Hypothesis 2: Education apps will have a higher number of reviews than Lifestyle apps
life_reviews <- mean(g_apps11$Reviews[g_apps11$Category=="LIFESTYLE"])
RC_Hypo <- t.test(g_apps11$Reviews[g_apps11$Category=="EDUCATION"],
alternative="greater",
mu=life_reviews,
conf.level=0.95)
RC_Hypo##
## One Sample t-test
##
## data: g_apps11$Reviews[g_apps11$Category == "EDUCATION"]
## t = -18.972, df = 73186, p-value = 1
## alternative hypothesis: true mean is greater than 4.535357
## 95 percent confidence interval:
## 4.358875 Inf
## sample estimates:
## mean of x
## 4.372955# Let's plot the difference
Edu <- g_apps11$Reviews[g_apps11$Category =="EDUCATION"]
Life <- g_apps11$Reviews[g_apps11$Category == "LIFESTYLE"]
plot(density(Edu), main = "Difference between Education & Lifestyle Apps", lwd= 3, col= "#00DCFF", xlab = "Log of Reviews")
lines(density(Life), col="#F83648", lwd=3)
legend("topright", c("Education", "lifestyle"), col = c("#00DCFF", "#F83648"), pch = c(19,19), cex = 0.8)
I will accept the null hypothesis for this test as the p-value is equal to 1.
# Hypothesis 3: On average, Paid apps will be rated higher than free apps.
g_apps12 <- g_apps11
g_apps12 %>% group_by(Price) %>% summarise(avg = mean(Rating), median = median(Rating), std = sd(Rating))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 2 x 4
## Price avg median std
## <fct> <dbl> <dbl> <dbl>
## 1 Free 4.35 4.40 0.440
## 2 Paid 4.39 4.45 0.420boxplot(Rating~Price, data = g_apps12, main="Boxplot of Installs by Rating",
col = c("#00DCFF", "#F83648")) #Very similar results
rat_price.aov <- aov(Rating~Price, data=g_apps11)
rat_price.aov## Call:
## aov(formula = Rating ~ Price, data = g_apps11)
##
## Terms:
## Price Residuals
## Sum of Squares 16.65 48724.43
## Deg. of Freedom 1 252609
##
## Residual standard error: 0.4391865
## Estimated effects may be unbalancedsummary(rat_price.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Price 1 17 16.651 86.33 <0.0000000000000002 ***
## Residuals 252609 48724 0.193
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(rat_price.aov)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Rating ~ Price, data = g_apps11)
##
## $Price
## diff lwr upr p adj
## Paid-Free 0.03953342 0.03119399 0.04787285 0plot(rat_price.aov)
I will reject the null hypothesis for this test. There is a statistically significant differences between the ratings of free and paid apps. Paid apps actually have a higher rating on average than free apps. Diagnostics plots suggest that the ANOVA test results are valid.
# Hypothesis 4: Apps Rated Mature will have more reviews than apps for Everyone
g_apps12 %>% group_by(Content.Rating) %>% summarise(avg = mean(Reviews), median = median(Reviews), std = sd(Reviews))## `summarise()` ungrouping output (override with `.groups` argument)## # A tibble: 2 x 4
## Content.Rating avg median std
## <fct> <dbl> <dbl> <dbl>
## 1 Everyone 4.70 4.52 2.54
## 2 Mature 5.48 5.30 2.87boxplot(Reviews~Content.Rating, data = g_apps12, main = "Boxplot of # of Reviews by Content Rating",
col=c("#00DCFF", "#F83648")) #Looks like mature apps get more reviews on average
rev_content.aov <- aov(Reviews~Content.Rating, data=g_apps11)
summary(rev_content.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## Content.Rating 1 13112 13112 1979 <0.0000000000000002 ***
## Residuals 252609 1673956 7
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1TukeyHSD(rev_content.aov)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Reviews ~ Content.Rating, data = g_apps11)
##
## $Content.Rating
## diff lwr upr p adj
## Mature-Everyone 0.779582 0.7452323 0.8139318 0plot(rev_content.aov)
I reject the null hypothesis for this test. Mature apps have higher reviews than apps for Everyone.
# Hypothesis 5: Apps with higher number of Installs will have a higher number of reviews
g_apps12$Installs <- as.character(g_apps12$Installs)
g_apps12$InstallCat <- rep(NA, nrow(g_apps12))
g_apps12$InstallCat[g_apps12$Installs %in% c("100000-1000000","1000000+")] <- "High"
g_apps12$InstallCat[g_apps12$Installs %in% c("10000-100000","1000-10000","0-500")] <- "Low"
g_apps12$InstallCat <- as.factor(g_apps12$InstallCat)
g_apps12$Installs <- as.factor(g_apps12$Installs)
summary(g_apps12$InstallCat)## High Low
## 62708 189903low_mean <- mean(g_apps12$Reviews[g_apps12$InstallCat == "Low"])
RI_Hypo <- t.test(g_apps12$Reviews[g_apps12$InstallCat=="High"],
alternative="greater",
mu=low_mean,
conf.level=0.95)
RI_Hypo##
## One Sample t-test
##
## data: g_apps12$Reviews[g_apps12$InstallCat == "High"]
## t = 678.53, df = 62707, p-value < 0.00000000000000022
## alternative hypothesis: true mean is greater than 3.693875
## 95 percent confidence interval:
## 8.047836 Inf
## sample estimates:
## mean of x
## 8.058416# Let's plot the difference
High_Installs <- g_apps12$Reviews[g_apps12$InstallCat =="High"]
Low_Installs <- g_apps12$Reviews[g_apps12$InstallCat == "Low"]
plot(density(High_Installs), main = "Number of Reviews for High & Low Apps", lwd= 3, col= "#00DCFF", xlab = "Log of Reviews")
lines(density(Low_Installs), col="#F83648", lwd=3)
legend("topright", c("High Installs", "Low Installs"), col = c("#00DCFF", "#F83648"), pch = c(19,19), cex = 0.8)
Test results show that we can reject the null hypothesis. Apps with higher installs recieve more reviews on average.
I will also use this created category for logistic regression to determine what variables are best for predicting whether or not an app will recieve a high or low amount of downloads.
Regression
options(scipen = 99)
g_apps13 <- g_apps12
g_mod0 <- glm(InstallCat~1, data = g_apps13, family = "binomial")
g_mod <- glm(InstallCat ~ Rating, data=g_apps13, family = "binomial")
summary(g_mod)$coef## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.5498513 0.04449110 -34.83509 7.161995e-266
## Rating 0.6151776 0.01030832 59.67777 0.000000e+001-logLik(g_mod)/logLik(g_mod0)# Using a calculation for McFaddens R Squared to figure out how much of the variance can be explained by this model.## 'log Lik.' 0.01253825 (df=2)I start with simple logistic regression to determine if ratings alone would be a good predictor for installs. The coefficient for rating shows a positive relationship between these two variables. As the rating of an app increases, the log likelihood that the number of Install will increase also increases. These results are statistically significant witha p-value less than 0.05.
By using McFadsdens R squared calculation for logistic regression, I see that the simple logistic regression model only explains about 1% of the variance in Installs. I will need a multiple logistic regression model to improve accuracy.
null <- glm(Installs ~ 1, data = g_apps13, family = "binomial") # first model
full <- glm(Installs ~ Category + Reviews + Rating + Size.Groups + Price + Content.Rating, data= g_apps13, family = "binomial") # second model
step(null, scope=list(lower=null, upper=full), direction="forward") # forward selection## Start: AIC=213565.1
## Installs ~ 1
##
## Df Deviance AIC
## + Reviews 1 100229 100233
## + Rating 1 188315 188319
## + Price 1 210157 210161
## + Size.Groups 4 211995 212005
## + Category 3 213197 213205
## + Content.Rating 1 213366 213370
## <none> 213563 213565
##
## Step: AIC=100233.4
## Installs ~ Reviews
##
## Df Deviance AIC
## + Price 1 93444 93450
## + Rating 1 96644 96650
## + Category 3 100083 100093
## + Size.Groups 4 100208 100220
## <none> 100229 100233
## + Content.Rating 1 100229 100235
##
## Step: AIC=93450.38
## Installs ~ Reviews + Price
##
## Df Deviance AIC
## + Rating 1 89612 89620
## + Category 3 93357 93369
## + Size.Groups 4 93392 93406
## <none> 93444 93450
## + Content.Rating 1 93444 93452
##
## Step: AIC=89619.95
## Installs ~ Reviews + Price + Rating
##
## Df Deviance AIC
## + Category 3 89480 89494
## + Size.Groups 4 89576 89592
## <none> 89612 89620
## + Content.Rating 1 89611 89621
##
## Step: AIC=89493.79
## Installs ~ Reviews + Price + Rating + Category
##
## Df Deviance AIC
## + Size.Groups 4 89444 89466
## + Content.Rating 1 89476 89492
## <none> 89480 89494
##
## Step: AIC=89465.86
## Installs ~ Reviews + Price + Rating + Category + Size.Groups
##
## Df Deviance AIC
## + Content.Rating 1 89439 89463
## <none> 89444 89466
##
## Step: AIC=89463.23
## Installs ~ Reviews + Price + Rating + Category + Size.Groups +
## Content.Rating##
## Call: glm(formula = Installs ~ Reviews + Price + Rating + Category +
## Size.Groups + Content.Rating, family = "binomial", data = g_apps13)
##
## Coefficients:
## (Intercept) Reviews PricePaid
## 2.57764 1.59061 -2.98005
## Rating CategoryENTERTAINMENT CategoryLIFESTYLE
## -1.09773 -0.21786 -0.17365
## CategoryPRODUCTIVITY Size.Groups0-4M Size.Groups4M-8.3M
## -0.24313 -0.25197 -0.34222
## Size.Groups8.3M-19M Size.Groups19M-334M Content.RatingMature
## -0.30781 -0.29209 0.06937
##
## Degrees of Freedom: 252610 Total (i.e. Null); 252599 Residual
## Null Deviance: 213600
## Residual Deviance: 89440 AIC: 89460step(full, data=g_apps13, direction="backward") # backward selection## Start: AIC=89463.23
## Installs ~ Category + Reviews + Rating + Size.Groups + Price +
## Content.Rating
##
## Df Deviance AIC
## <none> 89439 89463
## - Content.Rating 1 89444 89466
## - Size.Groups 4 89476 89492
## - Category 3 89574 89592
## - Rating 1 93305 93327
## - Price 1 96382 96404
## - Reviews 1 182831 182853##
## Call: glm(formula = Installs ~ Category + Reviews + Rating + Size.Groups +
## Price + Content.Rating, family = "binomial", data = g_apps13)
##
## Coefficients:
## (Intercept) CategoryENTERTAINMENT CategoryLIFESTYLE
## 2.57764 -0.21786 -0.17365
## CategoryPRODUCTIVITY Reviews Rating
## -0.24313 1.59061 -1.09773
## Size.Groups0-4M Size.Groups4M-8.3M Size.Groups8.3M-19M
## -0.25197 -0.34222 -0.30781
## Size.Groups19M-334M PricePaid Content.RatingMature
## -0.29209 -2.98005 0.06937
##
## Degrees of Freedom: 252610 Total (i.e. Null); 252599 Residual
## Null Deviance: 213600
## Residual Deviance: 89440 AIC: 89460step(null, scope = list(upper=full), data=g_apps13, direction="both") # Stepwise selection## Start: AIC=213565.1
## Installs ~ 1
##
## Df Deviance AIC
## + Reviews 1 100229 100233
## + Rating 1 188315 188319
## + Price 1 210157 210161
## + Size.Groups 4 211995 212005
## + Category 3 213197 213205
## + Content.Rating 1 213366 213370
## <none> 213563 213565
##
## Step: AIC=100233.4
## Installs ~ Reviews
##
## Df Deviance AIC
## + Price 1 93444 93450
## + Rating 1 96644 96650
## + Category 3 100083 100093
## + Size.Groups 4 100208 100220
## <none> 100229 100233
## + Content.Rating 1 100229 100235
## - Reviews 1 213563 213565
##
## Step: AIC=93450.38
## Installs ~ Reviews + Price
##
## Df Deviance AIC
## + Rating 1 89612 89620
## + Category 3 93357 93369
## + Size.Groups 4 93392 93406
## <none> 93444 93450
## + Content.Rating 1 93444 93452
## - Price 1 100229 100233
## - Reviews 1 210157 210161
##
## Step: AIC=89619.95
## Installs ~ Reviews + Price + Rating
##
## Df Deviance AIC
## + Category 3 89480 89494
## + Size.Groups 4 89576 89592
## <none> 89612 89620
## + Content.Rating 1 89611 89621
## - Rating 1 93444 93450
## - Price 1 96644 96650
## - Reviews 1 184785 184791
##
## Step: AIC=89493.79
## Installs ~ Reviews + Price + Rating + Category
##
## Df Deviance AIC
## + Size.Groups 4 89444 89466
## + Content.Rating 1 89476 89492
## <none> 89480 89494
## - Category 3 89612 89620
## - Rating 1 93357 93369
## - Price 1 96414 96426
## - Reviews 1 184493 184505
##
## Step: AIC=89465.86
## Installs ~ Reviews + Price + Rating + Category + Size.Groups
##
## Df Deviance AIC
## + Content.Rating 1 89439 89463
## <none> 89444 89466
## - Size.Groups 4 89480 89494
## - Category 3 89576 89592
## - Rating 1 93307 93327
## - Price 1 96387 96407
## - Reviews 1 183080 183100
##
## Step: AIC=89463.23
## Installs ~ Reviews + Price + Rating + Category + Size.Groups +
## Content.Rating
##
## Df Deviance AIC
## <none> 89439 89463
## - Content.Rating 1 89444 89466
## - Size.Groups 4 89476 89492
## - Category 3 89574 89592
## - Rating 1 93305 93327
## - Price 1 96382 96404
## - Reviews 1 182831 182853##
## Call: glm(formula = Installs ~ Reviews + Price + Rating + Category +
## Size.Groups + Content.Rating, family = "binomial", data = g_apps13)
##
## Coefficients:
## (Intercept) Reviews PricePaid
## 2.57764 1.59061 -2.98005
## Rating CategoryENTERTAINMENT CategoryLIFESTYLE
## -1.09773 -0.21786 -0.17365
## CategoryPRODUCTIVITY Size.Groups0-4M Size.Groups4M-8.3M
## -0.24313 -0.25197 -0.34222
## Size.Groups8.3M-19M Size.Groups19M-334M Content.RatingMature
## -0.30781 -0.29209 0.06937
##
## Degrees of Freedom: 252610 Total (i.e. Null); 252599 Residual
## Null Deviance: 213600
## Residual Deviance: 89440 AIC: 894601-logLik(full)/logLik(null) # Using a calculation for McFaddens R Squared to figure out how much of the variance can be explained by this model.## 'log Lik.' 0.5812048 (df=12)I used forward selection, backwards elimination and stepwise regression to find the best model for Installs prediction. Each method returned the same model with the same AIC value of 89460. The final model below uses all relevant variables in the dataset however, McFaddens R squared calculation shows that it only explains about 58% of the variance in the Install variable.
final <- glm(formula = Installs ~ Reviews + Price + Rating + Category +
Size.Groups + Content.Rating, family = "binomial", data = g_apps13)
summary(final)##
## Call:
## glm(formula = Installs ~ Reviews + Price + Rating + Category +
## Size.Groups + Content.Rating, family = "binomial", data = g_apps13)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.4283 0.0069 0.0597 0.2439 3.5785
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.577643 0.107844 23.902 < 0.0000000000000002
## Reviews 1.590614 0.008831 180.120 < 0.0000000000000002
## PricePaid -2.980053 0.036327 -82.034 < 0.0000000000000002
## Rating -1.097728 0.018374 -59.745 < 0.0000000000000002
## CategoryENTERTAINMENT -0.217857 0.023541 -9.254 < 0.0000000000000002
## CategoryLIFESTYLE -0.173653 0.023423 -7.414 0.000000000000123
## CategoryPRODUCTIVITY -0.243129 0.024475 -9.934 < 0.0000000000000002
## Size.Groups0-4M -0.251971 0.066287 -3.801 0.000144
## Size.Groups4M-8.3M -0.342221 0.066499 -5.146 0.000000265756169
## Size.Groups8.3M-19M -0.307805 0.066705 -4.614 0.000003941567053
## Size.Groups19M-334M -0.292086 0.066933 -4.364 0.000012779868712
## Content.RatingMature 0.069374 0.032315 2.147 0.031811
##
## (Intercept) ***
## Reviews ***
## PricePaid ***
## Rating ***
## CategoryENTERTAINMENT ***
## CategoryLIFESTYLE ***
## CategoryPRODUCTIVITY ***
## Size.Groups0-4M ***
## Size.Groups4M-8.3M ***
## Size.Groups8.3M-19M ***
## Size.Groups19M-334M ***
## Content.RatingMature *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 213563 on 252610 degrees of freedom
## Residual deviance: 89439 on 252599 degrees of freedom
## AIC: 89463
##
## Number of Fisher Scoring iterations: 8As we can see in the final model, all variables included in the model are statistically significant. Test data can be introduced to make predictions and test the accuracy of the model but that is beyond the scope of this project. As of right now the McFaddens R squared calcuation shows that the model explains 58% of the variance in Installs. I could also change the probability threshold to be greater than 0.5 and see if that improves the model accuracy.
In sum, we see that all models used in this dataset were important in predicting the amount of install an app would receive. More data on these apps could be included in the data to balance out some of the disproportionate variable and make a more accurate prediction. App developers could also benefit from more data on metrics that explain consumers are using these apps once they have been installed. Further analysis is needed but the analysis in this report is a great start.